Talk:Bramble–Hilbert lemma

A fact from Bramble–Hilbert lemma appeared on Wikipedia's Main Page in the Did you know column on 1 November 2007. The text of the entry was as follows:

Did you know... that in numerical analysis, the error of an approximation of a function $\textstyle u$ by a polynomial of order at most $\textstyle m-1$ in terms of derivatives of $\textstyle u$ of order $\textstyle m$ is bound by the Bramble-Hilbert lemma?

A record of the entry may be seen at Wikipedia:Recent additions/2007/November.

Wikipedia

lemma dilemma[edit]

I've never been to math camp but would like to know what a lemma is, what it does and why is it important. If anyone can introduce me to it in lay language, that'd be way cool. Julia Rossi 11:00, 1 November 2007 (UTC)[reply]

Never mind, I identified it and contextualised it with a see also section.Julia Rossi 22:19, 1 November 2007 (UTC)[reply]

Lemma is an auxiliary mathematical statement that is useful to prove other things but is not primarily of interest by itself. Thus, error estimates for finite elements are theorems; lemmas help us get there. In parallel to programming, the whole product would be a theorem, while library subroutines would be lemmas. In a way, if you call something lemma or theorem or proposition is a matter of taste. Jmath666 23:32, 1 November 2007 (UTC)[reply]

Hi again. Give the swift deletions, I hope I haven't stumbled into an article fiercely protected by its creator who feels my good-faith edit is lowering the tone. I wasn't tinkering with the substance, just minutely enhancing the wording which wikipedia invites us to do. I see the descriptive "theorem" (as per topic Lemma) that I placed in the text is gone. Also gone is the "see also" connecting it to the sub topics of math in the pedia. The problem as I see it is that wikipedia is not a text book as such, but a wide ranging encyclopedia. So, in your words, "if you call something lemma or theorem or proposition is a matter of taste" then, would it hurt to include a more generally recognised term to amplify meaning without it being tautology? I suggest that lemma is a cool technical term for mathiacs, "proposition" is cool for academics, "theorem" is recognisable for high school people. If you don't mind, I'd like "theorem" returned as an accessible, descriptive term, and the see also section if it doesn't offend your protective instincts for the article. What do you say? You could even revert it to that yourself.

One more point is that I like your studied delineation above – a lot – because i really learned something. Is there somewhere either in this article or in the Lemma section or somewhere in pedia, that you could put this? (I hope you give some thought to my case; others do the, "What the...! Can we have it in plain English?" if you prefer. I like to find a balance.)Julia Rossi 23:10, 3 November 2007 (UTC)[reply]

Actually, I did not delete your edits, I appreciate them and incorporated your ideas in a hopefully a better way, look at the diff. Your "See also lemma" has become wikilink "lemma" on top, and your "See also List of theorems" has become "category:Lemmas". Now lemma explains exactly what I said in other words. There are many pages with this or that lemma; none of them is the proper place for a general discourse of what "lemma" means. You can edit lemma if you like to get into that. Regarding "BH lemma ... is a theorem" that sounds weird, because theorem is not a more general term than lemma, just a different word for the same. A more general term would be proposition or statement or result, or, in this context, estimate. (That's how mathematicians use those words. Sorry. Can't change that. ) But why make the sentence more complicated and longer? Besides the grammar of the sentence with the added word "theorem" was wrong. Jmath666 04:07, 4 November 2007 (UTC)[reply]

In fact "see also" linking to lists of lemmas and theorems would not be a bad idea but 1. such lists are generated by the category mechanism automatically which is way better and 2. are you going to do it for all pages with lemmas or theorem? No. 1 is really an issue for Wikipedia_talk:WikiProject_Mathematics. Thanks for bringing this to my attention. And no, I am aware of the danger of becoming a fierce defender of some page and try not to. Jmath666 04:29, 4 November 2007 (UTC)[reply]

"2. are you going to do it for all pages with lemmas or theorem?" Do I have to? "Grammatically wrong". "I am aware of the danger of becoming a fierce defender of some page and try not to". Hmmm. C ya. Julia Rossi 07:19, 4 November 2007 (UTC)[reply]

"is a theorem named after James H. Bramble and Stephen R. Hilbert, bounds the error of an approximation of a function" Ok I missed the comma. It is run-on sentence anyway. Jmath666 12:27, 4 November 2007 (UTC)[reply]

Dependence of the constant[edit]

The constant is made dependent of the whole domain. I suppose it should only depend on the dimension of the domain, because otherwise, the introduction of the power of the diameter of the domain has vacous meaning. --131.220.99.58 (talk) 13:56, 30 October 2011 (UTC)[reply]

a constructive proof[edit]

Where is the definition of the d parameter used in the definition of chunkiness? Kakila (talk) 21:13, 28 September 2023 (UTC)[reply]